<?xml version="1.0" standalone="yes"?>
<Paper uid="P98-1019">
  <Title>Parsing Ambiguous Structures using Controlled Disjunctions and Unary Quasi-Trees</Title>
  <Section position="3" start_page="124" end_page="125" type="intro">
    <SectionTitle>
2 Ambiguity and Disjunctions
</SectionTitle>
    <Paragraph position="0"> Several techniques have been proposed for the interpretation and the control of disjunctive structures. For example, delaying the evaluation of the disjunctive formulae until obtaining enough information allows partial disambiguation (cf. (Karttunen84)). Another solution consists in converting the disjunctive formulae into a conjunctive form (using negation) as proposed by (Nakazawa88) or (Maxwell91). We can also make use of the properties of the formula in order to eliminate inconsistencies.</Paragraph>
    <Paragraph position="1"> This approach, described in (Maxwell91), relies on the conversion of the original disjunctive formulae into a set of contexted constraints which allows, by the introduction of propositional variables (i) to convert the formulae into a conjunctive form, and (ii) to isolate a subset of formulae, the disjunctive residue (the negation of the unsatisfiable constraints). The problem of the satisfiability of the initial formula is then reduced to that of the disjunctive residue.</Paragraph>
    <Paragraph position="2"> This approach is fruitful and several methods rely on this idea to refer formulae with an index (a propositional variable, an integer, etc.). It is the case in particular with named disjunctions (see (DSrre90), (Krieger93) or (Gerdemann95)) which propose a compact representation of control phenomena and covariancy. null A named disjunction (noted hereafter ND) binds several disjunctive formulae with an index (the name of the disjunction). These formulae have the same arity and their disjuncts are ordered. They are linked by a covariancy relation: when one disjunct in a ND is selected (i.e. interpreted to true), then all the disjuncts occurring at the same position into the other formulae of the ND also have to be true. The example (1) presents the lexical entry of the german determiner den. The covariation is indicated by three disjunctive formulae composing the named disjunction indexed by 1.</Paragraph>
    <Paragraph position="4"> But the named disjunction technique also has some limits. In particular, NDs have to represent all the relations between formulae in a covariant way. This leads to a lot of redundancy and a loss of the compactness in the sense that the disjuncts don't contain anymore the possible values but all the possible variancies according to the other formulae. null  Some techniques has been proposed in order to eliminate this drawback and in particular: the dependency group representation (see (Griffith96)) and the controlled disjunctions (see (Blache97)). The former relies on an enrichment of the Maxwell and Kaplan's contexted constraints. In this approach, constraints are composed of the conjunction of base constraints (corresponding to the initial disjunctive form) plus a control formula representing the way in which values are choosen. The second approach, described in the next section, consists in a specific representation of control relations relying on a clear distinction between (i) the possible values (the disjuncts) and (ii) the relations between these ambiguous values and other elements of the structure. This approach allows a direct implementation of the implication relations (i.e. the oriented controls) instead of simple covariancies.</Paragraph>
  </Section>
class="xml-element"></Paper>